Nuprl Lemma : pi_term_ind_wf_simple
∀[A:Type]. ∀[v:pi_term()]. ∀[zero:A]. ∀[comm:pre:pi_prefix() ⟶ body:pi_term() ⟶ A ⟶ A].
∀[option,par:left:pi_term() ⟶ right:pi_term() ⟶ A ⟶ A ⟶ A]. ∀[rep:body:pi_term() ⟶ A ⟶ A]. ∀[new:name:Name
                                                                                                       ⟶ body:pi_term()
                                                                                                       ⟶ A
                                                                                                       ⟶ A].
  (... ∈ A)
Proof
Definitions occuring in Statement : 
pi_term_ind: pi_term_ind(v;zero;pre,body,rec1....;left,right,rec2,rec3....;left,right,rec4,rec5....;body,rec6....;name,body,rec7....)
, 
pi_term: pi_term()
, 
pi_prefix: pi_prefix()
, 
name: Name
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s1;s2;s3;s4]
, 
so_apply: x[s1;s2;s3]
, 
so_apply: x[s1;s2]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
subtype_rel: A ⊆r B
, 
true: True
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
guard: {T}
Latex:
\mforall{}[A:Type].  \mforall{}[v:pi\_term()].  \mforall{}[zero:A].  \mforall{}[comm:pre:pi\_prefix()  {}\mrightarrow{}  body:pi\_term()  {}\mrightarrow{}  A  {}\mrightarrow{}  A].
\mforall{}[option,par:left:pi\_term()  {}\mrightarrow{}  right:pi\_term()  {}\mrightarrow{}  A  {}\mrightarrow{}  A  {}\mrightarrow{}  A].  \mforall{}[rep:body:pi\_term()  {}\mrightarrow{}  A  {}\mrightarrow{}  A].
\mforall{}[new:name:Name  {}\mrightarrow{}  body:pi\_term()  {}\mrightarrow{}  A  {}\mrightarrow{}  A].
    (...  \mmember{}  A)
Date html generated:
2016_05_17-AM-11_22_49
Last ObjectModification:
2015_12_29-PM-06_55_00
Theory : event-logic-applications
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